Answer:
(x - 3)² = 10
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
x² = 6x + 1
<u>Step 2: Rewrite</u>
- Subtract 6x on both sides: x² - 6x = 1
- Complete the Square: x² - 6x + 9 = 1 + 9
- Factor: (x - 3)² = 10
Answer:
First option:
Second option:
Fourth option:
Step-by-step explanation:
Rewrite each equation in the form and then use the Discriminant formula for each equation. This is:
1) For :
Then:
Since this equation has no real solutions, but has two complex solutions.
2) For :
Then:
Since this equation has no real solutions, but has two complex solutions.
3) For :
Then:
Since this equation has one real solution.
4) For :
Then:
Since , this equation has no real solutions, but has two complex solutions.
Answer: $50
Step-by-step explanation: Draw a line through the apparent center of the scattered dots. See where that line intersects 9 in the time scale (x-axis numbers) and the dollars earned scale (y-axis numbers)
It could be 50 or 55, but since there are a few more dots below the apparent midline, it may be best to use the lower estimate.
Answer:
Step-by-step explanation:
Our inequality is |125-u| ≤ 30. Let's separate this into two. Assuming that (125-u) is positive, we have 125-u ≤ 30, and if we assume that it's negative, we'd have -(125-u)≤30, or u-125≤30.
Therefore, we now have two inequalities to solve for:
125-u ≤ 30
u-125≤30
For the first one, we can subtract 125 and add u to both sides, resulting in
0 ≤ u-95, or 95≤u. Therefore, that is our first inequality.
The second one can be figured out by adding 125 to both sides, so u ≤ 155.
Remember that we took these two inequalities from an absolute value -- as a result, they BOTH must be true in order for the original inequality to be true. Therefore,
u ≥ 95
and
u ≤ 155
combine to be
95 ≤ u ≤ 155, or the 4th option
Answer:
1.83% probability there are no car accidents on that stretch on Monday
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
The number of accidents on a certain section of I-40 averages 4 accidents per weekday independent across weekdays.
This means that
What is the probability there are no car accidents on that stretch on Monday?
This is P(X = 0).
1.83% probability there are no car accidents on that stretch on Monday